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    Les chevaliers de Dieu

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    D'Alessandro Vincenzo. Les chevaliers de Dieu . In: Annales de Normandie, 58ᵉ année, n°1-2, 2008. pp. 59-66

    Theory of electrothermal behavior of bipolar transistors: Part I - Single-finger devices

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    A detailed theoretical and numerical analysis of the electrothermal behavior of single-finger bipolar transistors is proposed. Two models of different complexities are introduced to investigate self-heating effects in bipolar junction transistors (BJTs) and heterojunction bipolar transistors (HBTs) biased with a constant base–emitter voltage source or with a constant base current source. In the constant base–emitter voltage case, simple relations are derived for determining the onset of the flyback behavior in the output characteristics which defines the boundary of the safe operating region. The model indicates that the flyback behavior disappears at high BE values, and predicts a thermal hysteresis phenomenon at high currents. It is also shown that at high current levels the electrothermal behavior is dominated by ohmic base pushout. If a constant base current is applied, the model shows that both BJTs and HBTs are unconditionally thermally stable. The transient behavior is also considered, and the temperature evolution is investigated for different bias conditions. The model shows that, if the device is biased in the thermally unstable region, thermal breakdown occurs within a finite time instant in the limit case of a zero ballast resistance. Finally, the reduction in the safe operating area due to avalanche effects and to the temperature dependence of thermal conductivity is discussed, and a simplified model is proposed

    Fast analytical modeling of dynamic thermal behavior of semiconductor devices and circuits

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    This paper presents a set of closed-form analytical expressions to approximate the transient solution to the heat equation without requiring any computationally intensive series summation. The parameters of these expressions can be easily extracted from the physical layout for constructing a thermal impedance matrix to be used in a self-consistent electrothermal circuit simulation of a large number of heat sources. These formulations are derived by assuming a small heat source compared to the chip area in a homogeneous chip with the boundary conditions of an adiabatic top and an isothermal bottom. The derivation allows heat sources to be located at a certain depth from the chip top. The expressions have been verified by comparison with 3-D numerical simulations
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